I. To determine the safety and toxicity of the intravenous administration of an Edmonston vaccine strain measles virus engineered to express the thyroidal sodium iodide symporter (MV-NIS) when administered with or without cyclophosphamide in patients with relapsed or refractory multiple myeloma. (Phase I) II. To evaluate the confirmed response rate of MV-NIS in patients with relapsed or refractory multiple myeloma. (Phase I) III. To further evaluate the adverse event profile of MV-NIS in patients with relapsed or refractory multiple myeloma. (Phase II) IV. To evaluate overall survival, failure-free survival and progression-free survival. (Phase II)